Monolithic hp Space-Time Multigrid Preconditioning for a Newton-Krylov Solver for Space-Time FEM applied to Navier-Stokes Equations

We present a monolithic hp space-time multigrid method for tensor-product space-time finite element discretizations of the incompressible Navier-Stokes equations. The formulation employs inf-sup stable velocity-pressure pairs in space, a discontinuous Galerkin discretization in time, and combined geometric and polynomial coarsening in both space and time. Nonlinearity due to the convective term is treated by Newton linearization, and the resulting space-time systems are solved by GMRES preconditioned with an hp space-time multigrid method in a matrix-free deal.II implementation using a space-time Vanka-type smoother for the velocity-pressure coupling. The tensor-product structure enables efficient sum-factorization for residual and Jacobian evaluation, and numerical experiments show mesh-independent convergence and robust performance across a range of flow regimes.

Contatto:
paolo.zunino@polimi.it